Transcript
Page 1: Is Multipath Routing Really a Panacea?

Is Multipath Routing Really a Panacea?

Deep Medhi

Computer Science & Electrical Engineering DepartmentUniversity of Missouri-Kansas City, USA

[email protected] association with Xuan Liu, Sudhir Mohanraj, and Michał Pioro

Supported in part by NSF Grant # CNS-0916505

CNSM Keynote: 11 November 2015

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Keynote dedicatedin memory ofKaren Medhi

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Manhattan, NY

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Going between Two points in Manhattan, NY

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Going between Two points in Manhattan, NY: one path

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Going between Two points in Manhattan: two paths

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Going between Two points in Manhattan: three paths

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Going between Several points in Manhattan, NY

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Going between *ANY* two points in Manhattan, NY

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Question:

At instant of time, is multipath routing beneficial?

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What Multipath Routing is NOT

Take one path in the morning, another path in the evening – thisis NOT multipath routing

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Multipath Routing: A Common Belief

Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

An alternative considered in this context is single-pathrouting (non-split routing of the demands).— Many ISPs prefer (for troubleshooting)Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.Question: Does it? When? How much?Taking a Traffic Engineering Perspective...

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Multipath Routing: A Common Belief

Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

An alternative considered in this context is single-pathrouting (non-split routing of the demands).— Many ISPs prefer (for troubleshooting)

Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.Question: Does it? When? How much?Taking a Traffic Engineering Perspective...

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Multipath Routing: A Common Belief

Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

An alternative considered in this context is single-pathrouting (non-split routing of the demands).— Many ISPs prefer (for troubleshooting)Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.

Question: Does it? When? How much?Taking a Traffic Engineering Perspective...

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Multipath Routing: A Common Belief

Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

An alternative considered in this context is single-pathrouting (non-split routing of the demands).— Many ISPs prefer (for troubleshooting)Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.Question: Does it? When? How much?

Taking a Traffic Engineering Perspective...

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Multipath Routing: A Common Belief

Multipath routing (load sharing): split routing where eachnode-to-node traffic can be send among accessible paths.

An alternative considered in this context is single-pathrouting (non-split routing of the demands).— Many ISPs prefer (for troubleshooting)Common belief: multipath routing, as compared withsingle-path routing, gives a significantly better opportunityto control the link loads and in this way effectively optimizevarious traffic objectives.Question: Does it? When? How much?Taking a Traffic Engineering Perspective...

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A 3-node Example: Single Demand (Commodity)

1

3

2

10

10

10Capacity

15

Traffic Volumebetween 1 and 2

Easy to see that 15 units of traffic would need to be splitbetween the paths 1-2 and 1-3-2.

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3-node example: All pairs with traffic

1

3

2

Capaci

ty = 10Capacity = 10

Capacity = 15

Traffic = 5

Traffic = 7Traffic =

10

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Min Cost Routing: (i) Illustration for 3-node network: all pair traffic

Linear Programming Formulation:Minimize x12 + 2 x132 + x13 + 2 x123 + x23 + 2 x213

subject to

d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213 <= 10c13: x132 + x13 + x213 <= 10c23: x132 + x123 + x23 <= 15Boundsx12 >= 0x132 >= 0x13 >= 0x123 >= 0x23 >= 0x213 >= 0End

1

3

2

Capaci

ty = 10

Capacity = 10

Capacity = 15

Traffic = 5

Traffic = 7Traffic =

10For each pair, the first (direct) path is cheaper than the second path.Solution: x12 = 5, x13 = 10, x23 = 7 3 positive path-flows

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3-node example: All pairs with traffic

1

3

2

Capaci

ty = 10

Capacity = 10Capacity = 15

Traffic = 5

Traffic = 7Traffic =

10

Is it possible for each pair to use both the direct and alternatetwo-link paths with positive flows at optimality?

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Min Cost Routing: (ii) 3-node net (swap path cost)

Minimize 2 x12 + x132 + 2 x13 + x123 + 2 x23 + x213subject to

d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213 <= 10c13: x132 + x13 + x213 <= 10c23: x132 + x123 + x23 <= 15Boundsx12 >= 0x132 >= 0x13 >= 0x123 >= 0x23 >= 0x213 >= 0End

1

3

2

Capaci

ty = 10

Capacity = 10Capacity = 15

Traffic = 5

Traffic = 7Traffic =

10

Note: same traffic demand and link capacity as before; the path cost in objective ischanged. Solution: x12 = 1, x132 = 4, x13 = 3.5, x123 = 6.5, x23 = 4.5, x213 = 2.56 positive path-flows

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Is there a connection?

1) How does the number of positive flows at optimality relate tothe size of the problem?2) Does the objective function matter?

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Two Letters to Remember for the Rest of the Talk

D : Number of demands in a Network

L : Number of Links in a Network

NOTE:D = N(N − 1)/2 if every pair has traffic (bidirectional) in aN-node network

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Two Letters to Remember for the Rest of the Talk

D : Number of demands in a Network

L : Number of Links in a Network

NOTE:D = N(N − 1)/2 if every pair has traffic (bidirectional) in aN-node network

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D + L result: Min Cost Routing Multi-CommodityNetwork Flow

minx≥0

∑d∈D

∑p∈Pd

ξdp xdp (1a)

∑p∈Pd

xdp = hd , d ∈ D (demand) (1b)

∑d∈D

∑p∈Pd

δdp`xdp ≤ c`, ` ∈ L (capacity) (1c)

hd : traffic for demand ID d ∈ D (#(D) = D)c`: link capacity (#(L) = L)ξdp: unit path cost of path p for demand dδdp`: link-path indicator 0/1

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Min Cost Routing Multi-Commodity Network Flow

minx≥0

∑d∈D

∑p∈Pd

ξdp xdp∑p∈Pd

xdp = hd , d ∈ D (demand)

∑d∈D

∑p∈Pd

δdp`xdp ≤ c`, ` ∈ L (capacity)

D + L property

In vertex solutions in Linear Program, there are at most D + L positivepath-flows. (Proof skipped)

Corollary: There are at most L demands that require more than onepositive path-flow

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Quick Review: Feasible Region and vertices for a linear program

Objective

Feasible Region

Optimal Vertex

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Consider again the following illustration for the 3-nodemulti-commodity example:

d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213 <= 10c13: x132 + x13 + x213 <= 10c23: x132 + x123 + x23 <= 15x non-negative

Adding slack variables:

d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213 + s12 = 10c13: x132 + x13 + x213 + s13 = 10c23: x132 + x123 + x23 + s23 = 15x, s non-negative

Here, D = 3, L = 3. After adding slack variables, we have six (6) equations with nine(9) variables. This means that at most 6 variables can be positive at a basic feasiblesolution, and consequently, at optimality.

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CorollaryIf the optimization problem (1) is feasible, then at most L trafficpairs will have more than one path with non-zero flows atoptimality.

Proof:

From the theorem, we know that there are D + L non-zero flowvariables. Since there are a total of D pairs, at least one pathfor each pair must carry the traffic load. This then leaves uswith at most D + L− D = L pairs that has more than one pathswith non-zero flows.

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CorollaryIf the optimization problem (1) is feasible, then at most L trafficpairs will have more than one path with non-zero flows atoptimality.

Proof:

From the theorem, we know that there are D + L non-zero flowvariables. Since there are a total of D pairs, at least one pathfor each pair must carry the traffic load. This then leaves uswith at most D + L− D = L pairs that has more than one pathswith non-zero flows.

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Traffic Engineering Objectives (besides min costrouting)

Commonly used traffic engineering objectives for IP, MPLS,SDN networks:

Network Load Balancing (Minimize Maximum utilization),also known as Congestion MinimizationAverage Delay (Minimize Average Network Delay)

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Load Balancing Optimization: LP Formulation

min{x≥0,r}

r

subject to ∑p∈Pd

xdp = hd , d ∈ D∑d∈D

∑p∈Pd

δdp` xdp ≤ c`r , ` ∈ L

xdp ≥ 0, p = 1, 2, ...,Pd ,d = 1, 2, ...,D

(3)

Note: introduced a new variable r (load balancing variable)

We again have D + L constraints.

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LB: load balancing

minx≥0,r

r∑p∈Pd

xdp = hd , d ∈ D

∑d∈D

∑p∈Pd

δdp`xdp ≤ c`r , ` ∈ L

xdp ≥ 0, p = 1,2, ...,Pd , d = 1,2, ...,D

D + L − 1 property

In vertex solutions, there are at most D + L − 1 positive path-flows.

There are at most L − 1 demands that require more than one positivepath-flow.

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3-node Illustration for load balancing

Minimize rsubject to

d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213 <= 10 rc13: x132 + x13 + x213 <= 10 rc23: x132 + x123 + x23 <= 15 rBoundsx12 >= 0x132 >= 0x13 >= 0x123 >= 0x23 >= 0x213 >= 0End

1

3

2

Capaci

ty = 10

Capacity = 10Capacity = 15

Traffic = 5

Traffic = 7Traffic =

10

Solution: x12 = 4.125, x132 = 0.875, x13 = 6.625, x123 = 3.375, x23 = 7, r∗ = 0.75D + L− 1 = 3 + 3− 1 = 5

One pair always has single-path routing at optimality

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3-node Illustration for load balancing

Minimize rsubject to

d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213 <= 10 rc13: x132 + x13 + x213 <= 10 rc23: x132 + x123 + x23 <= 15 rBoundsx12 >= 0x132 >= 0x13 >= 0x123 >= 0x23 >= 0x213 >= 0End

1

3

2

Capaci

ty = 10

Capacity = 10Capacity = 15

Traffic = 5

Traffic = 7Traffic =

10

Solution: x12 = 4.125, x132 = 0.875, x13 = 6.625, x123 = 3.375, x23 = 7, r∗ = 0.75D + L− 1 = 3 + 3− 1 = 5 One pair always has single-path routing at optimality

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Minimize Average Delay (AD)

minx≥0,y≥0

∑∈L

y`c`−y`

subject to∑

p∈Pd

xdp = hd , d ∈ D∑d∈D

∑p∈Pd

δdp` xdp = y`, ` ∈ L(5)

Note: Objective is non-linear.

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D + L for non-linear AD

The D + L property holds for the non-linear AD problem!

minx≥0,y≥0

∑∈L

y`c`−y`

subject to∑

p∈Pd

xdp = hd , d ∈ D∑d∈D

∑p∈Pd

δdp` xdp = y`, ` ∈ L(6)

We’ve a proof!

Margins of this slide is too small to fit in the proof :)

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D + L for non-linear AD

The D + L property holds for the non-linear AD problem!

minx≥0,y≥0

∑∈L

y`c`−y`

subject to∑

p∈Pd

xdp = hd , d ∈ D∑d∈D

∑p∈Pd

δdp` xdp = y`, ` ∈ L(6)

We’ve a proof!

Margins of this slide is too small to fit in the proof :)

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Two Measures

What percentage of demand pairs have more than onepath at optimality?– MPM (Multipath Measure)

How far off is the single-path routing compared to multipathrouting?– Normalized Cost Overhead (COH)

COH =OPTSinglePath −OPTMultiPath

OPTMultiPath

NOTE: MPM = 0 −→ Single-Path Routing is Optimal

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Two Measures

What percentage of demand pairs have more than onepath at optimality?– MPM (Multipath Measure)How far off is the single-path routing compared to multipathrouting?– Normalized Cost Overhead (COH)

COH =OPTSinglePath −OPTMultiPath

OPTMultiPath

NOTE: MPM = 0 −→ Single-Path Routing is Optimal

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Two Measures

What percentage of demand pairs have more than onepath at optimality?– MPM (Multipath Measure)How far off is the single-path routing compared to multipathrouting?– Normalized Cost Overhead (COH)

COH =OPTSinglePath −OPTMultiPath

OPTMultiPath

NOTE: MPM = 0 −→ Single-Path Routing is Optimal

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MPM: multipath measure

definitionMPM is equal to the maximum percentage of demands that canhave more than one path with nonzero flow at optimal vertexsolutions.

MCR: MPM = LD

LB: MPM = L−1D

AD: MPM = LD

(max value = 100%)

MPM computed to optimality: to be denoted by MPM∗

MPM∗ ≤ MPM

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MPM: multipath measure

definitionMPM is equal to the maximum percentage of demands that canhave more than one path with nonzero flow at optimal vertexsolutions.

MCR: MPM = LD

LB: MPM = L−1D

AD: MPM = LD

(max value = 100%)

MPM computed to optimality: to be denoted by MPM∗

MPM∗ ≤ MPM

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Average vertex degree for Real-world ISP Networks

Topology Zoo Collection: the highest average vertex degree 4.5

RocketFuel Collection (PoP-level topology): the highest average vertex degree5.24

Use ”3N-Net” as an upper limit for theoretical MPM– L = 3N means average vertex degree is 6

Important to note: with L = O(N), D = O(N2)

MPM (=L/D) −→ 0 as N →∞

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Average vertex degree for Real-world ISP Networks

Topology Zoo Collection: the highest average vertex degree 4.5

RocketFuel Collection (PoP-level topology): the highest average vertex degree5.24

Use ”3N-Net” as an upper limit for theoretical MPM– L = 3N means average vertex degree is 6

Important to note: with L = O(N), D = O(N2)

MPM (=L/D) −→ 0 as N →∞

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Average vertex degree for Real-world ISP Networks

Topology Zoo Collection: the highest average vertex degree 4.5

RocketFuel Collection (PoP-level topology): the highest average vertex degree5.24

Use ”3N-Net” as an upper limit for theoretical MPM– L = 3N means average vertex degree is 6

Important to note: with L = O(N), D = O(N2)

MPM (=L/D) −→ 0 as N →∞

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Average vertex degree for Real-world ISP Networks

Topology Zoo Collection: the highest average vertex degree 4.5

RocketFuel Collection (PoP-level topology): the highest average vertex degree5.24

Use ”3N-Net” as an upper limit for theoretical MPM– L = 3N means average vertex degree is 6

Important to note: with L = O(N), D = O(N2)

MPM (=L/D) −→ 0 as N →∞

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Theoretical MPM

N = 4 N = 9 N = 16 N = 25 N = 36 N = 49 N = 100 N = 1024

D 6 36 120 300 630 1,176 4,950 523,776R(MCR/AD) 66.67 25.00 13.33 8.33 5.71 4.17 2.02 0.20R(LB) 50.00 22.22 12.50 8.00 5.56 4.08 2.00 0.20G(MCR/AD) 66.67 33.33 20.00 13.33 9.52 7.14 3.64 0.38G(LB) 50.00 30.56 19.17 13.00 9.37 7.06 3.62 0.383N(MCR/AD) 100.00 75.00 40.00 25.00 17.14 12.50 6.06 0.593N(LB) 83.33 72.22 39.17 24.67 16.98 12.41 6.04 0.59

MPM (in %) for different network sizes and topologies

D = N/(N-1)/2 (No. of demand pairs)R(Ring) L = N

G(Grid) L = 2N − 2√

N3N(3N-Net) L = 3N

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Special Results: Ring Network, uniform traffic/capacitycase (”Symmetric Ring”): LB Objective

In a ring network, every pair of nodes have two paths:clockwise and counter-clockwise.

If the number of nodes N is odd, then in a ring with uniformtraffic for all node pairs and link capacity (”symmetric ring”),only one path (minimum-hop shortest path) is used byeach pair at optimality for the LB objective. That is,MPM∗ = 0If the number of nodes N is even, then in a symmetric ringMPM∗ = 1

N−1

Same hold for AD objective too.

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Special Results: Ring Network, uniform traffic/capacitycase (”Symmetric Ring”): LB Objective

In a ring network, every pair of nodes have two paths:clockwise and counter-clockwise.If the number of nodes N is odd, then in a ring with uniformtraffic for all node pairs and link capacity (”symmetric ring”),only one path (minimum-hop shortest path) is used byeach pair at optimality for the LB objective. That is,MPM∗ = 0If the number of nodes N is even, then in a symmetric ringMPM∗ = 1

N−1

Same hold for AD objective too.

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Symmetric Ring - Odd number of nodes - Illustration(N = 5)

12

3

4

5

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Symmetric Ring - Even number of nodes - Illustration(N = 4)

1 2

34

No split for: 1:2, 2:3, 3:4, 1:4 greenequal split for: 1:3 (blue), 2:4 (brown)MPM∗ = 2/6 = 1/3

If N = 101, then MPM∗ = 1/100 = 1%

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A Series of Comprehensive Studies

Topologies: Ring, Grid, Example ISP topologiesTraffic distribution: uniform (U), uniform-perturbed (U-P),Elephant-mice (EM) traffic, Lognormal (LN) trafficNetwork Load: 0.4 to 0.95For each load, five traffic profiles generated randomlyFor Load Balancing Objective, we proved a traffic scalingproperty that the optimal solution doesn’t change.A few representative results presented here.

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A Representative set of resultsCases

All pair traffic (D = N(N − 1)/2)Limited pair traffic for Data Center NetworksWhat happens as we increase D from 1,2, ....,N(N − 1)/2

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Ring Topology: MPM∗ and COH

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Grid Topology: MPM∗ and COH

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Fully-Mesh Topology

Theoretical MPM: 100%

Symmetric Mesh: Uniform traffic, uniform capacity– Optimal is direct routing between any two nodes (single-path)

General Traffic– Use Sprint’s 43-node fully-mesh telephone backbone network– Traffic for different time of the day– MPM∗: 19% on average– MPM∗: as high at 41%

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Fat-tree Data Center Networks

A special structure: k -pod architecture

NOT all pairs of nodes have traffic

Only Edge Switches have traffic intra-data center case

9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8

17 18 19 20

Edge

Aggregation

Core

k -pod fat-tree topologyN = 5

4 k2

D = k4

8 −k2

4

L = k3

2

L = O(k3),D = O(k4) MPM = L/D → 0

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Fat-Tree Topology: MPM and MPM∗ for LB

9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8

17 18 19 20

Edge

Aggregation

Core

k N D L MPM MPM∗ COH MPM∗ COH(U) (U) (LN) (LN)

4 20 28 32 100.00 35.71 14.29 15.00 0.536 45 153 108 69.93 39.87 5.88 10.85 0.368 80 496 256 51.41 28.02 3.23 9.47 0.31

U:=uniform traffic, LN:=lognormal traffic;COH:=Cost Overhead in (%)

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What happens when we start from a single demand pair andcontinue to add more demand pairs until D = N(N − 1)/2

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MPM* for grid, lognormal N = 16,25,36

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

X: 1Y: 3.664

Demand Type: Lognormal (µ =16.6, σ=1.04 )

No. of Demand Pairs / Total Pairs

MP

M*

(%)

Grid: 16 NodesGrid: 25 NodesGrid: 36 Nodes

[Warning: In some cases, single-path routing was not run longenough to reach optimality.]

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MPM* for grid, lognormal N = 49,64,100

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

60

X: 0.4354Y: 2.068

Demand Type: Lognormal (µ =16.6, σ=1.04 )

No. of Demand Pairs/Total Pairs

MP

M*

(%)

Grid: 49 NodesGrid: 64 NodesGrid: 100 Nodes

[Warning: In some cases, single-path routing was not run longenough to reach optimality.]

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MPM* and COH for N = 16,25,36 (Grid, lognormal)

#ofDemandPairsMPM* COH(%) #ofDemandPairsMPM* COH(%) #ofDemandPairsMPM* COH(%)1 100.00 100.00 1 80 69.79 1 100.00 113.892 70.00 117.86 2 60 43.04 2 60.00 100.004 65.00 52.83 4 50 42.82 4 35.00 22.898 37.50 30.34 8 35 35.06 8 27.50 55.1716 25.00 24.16 16 18.75 12.92 16 25.00 30.6332 18.75 15.94 32 16.25 20.66 32 13.13 16.0764 9.06 3.36 64 13.438 10.62 64 12.81 4.09

120 4.83 0.00 128 7.966 1.11 128 7.81 1.01256 4.532 0.00 256 5.08 0.00300 3.664 0.00 512 3.75 0.00

630 2.32 0.00

16Nodes 36Nodes25Nodes

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MPM* and COH for N = 49,64,100 (Grid, lognormal)

#ofDemandPairsMPM*(%) Overhead(%)#ofDemandPairsMPM*(%) Overhead(%)#ofDemandPairsMPM*(%) Overhead(%)1 60.00 23.33 1 40.00 14.29 1 20.00 6.672 50.00 46.51 2 20.00 24.24 2 10.00 21.744 35.00 57.89 4 35.00 40.00 4 30.00 4.178 20.00 20.35 8 15.00 15.79 8 12.50 0.0016 15.00 6.95 16 8.75 4.30 16 13.75 5.7132 11.25 9.27 32 13.75 13.27 32 14.37 8.0064 9.06 22.49 64 9.69 14.75 64 8.75 18.52

128 7.66 7.66 128 4.84 0.68 128 5.00 0.00256 5.31 0.10 256 3.59 0.16 256 5.31 1.40512 2.07 0.00 512 3.40 0.63 512 2.42 0.001024 1.78 0.00 1024 1.11 0.50 1024 1.62 2.151176 1.26 0.00 2016 0.92 0.00 2048 0.98 0.11

4096 0.40 0.004950 0.34 0.00

100Nodes49Nodes 64Nodes

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Page 65: Is Multipath Routing Really a Panacea?

So, what went wrong in our thought process about thebenefit of multipath routing?

Our minds do play trick:)— We forget that others are using the network too— Remember the Manhattan Street Network

Often, smaller topologies were studied where multipath iscertainly beneficialFor large problems, heuristic algorithms were developed toshow the “benefit” of multipath routing– Problem is ....– Heuristic gives a false sense of benefit of multipathrouting since the solution is near optimal, but not anoptimal vertex solution!

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Page 66: Is Multipath Routing Really a Panacea?

So, what went wrong in our thought process about thebenefit of multipath routing?

Our minds do play trick:)— We forget that others are using the network too— Remember the Manhattan Street NetworkOften, smaller topologies were studied where multipath iscertainly beneficial

For large problems, heuristic algorithms were developed toshow the “benefit” of multipath routing– Problem is ....– Heuristic gives a false sense of benefit of multipathrouting since the solution is near optimal, but not anoptimal vertex solution!

MPR-SPR

Page 67: Is Multipath Routing Really a Panacea?

So, what went wrong in our thought process about thebenefit of multipath routing?

Our minds do play trick:)— We forget that others are using the network too— Remember the Manhattan Street NetworkOften, smaller topologies were studied where multipath iscertainly beneficialFor large problems, heuristic algorithms were developed toshow the “benefit” of multipath routing

– Problem is ....– Heuristic gives a false sense of benefit of multipathrouting since the solution is near optimal, but not anoptimal vertex solution!

MPR-SPR

Page 68: Is Multipath Routing Really a Panacea?

So, what went wrong in our thought process about thebenefit of multipath routing?

Our minds do play trick:)— We forget that others are using the network too— Remember the Manhattan Street NetworkOften, smaller topologies were studied where multipath iscertainly beneficialFor large problems, heuristic algorithms were developed toshow the “benefit” of multipath routing– Problem is ....– Heuristic gives a false sense of benefit of multipathrouting since the solution is near optimal, but not anoptimal vertex solution!

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Page 69: Is Multipath Routing Really a Panacea?

3-node Load Balancing example - revisit: optimal vs. near optimal solution

Minimize rsubject to

d12: x12 + x132 = 5d13: x13 + x123 = 10d23: x23 + x213 = 7c12: x12 + x123 + x213 <= 10c13: x132 + x13 + x213 <= 10c23: x132 + x123 + x23 <= 15End

1

3

2

Capaci

ty = 10

Capacity = 10

Capacity = 15

Traffic = 5

Traffic = 7Traffic =

10

Optimal r∗ = 0.75One demand is always single-path at optimality; In this case, pair 2:3 has single pathrouting, x23=7. Forcing this demand pair to take two paths will result in multipath forevery pair, but the solution is NOT optimal.Let’s say, x23 = 7− ε, and x213 = ε > 0. Then, the best r becomes 0.75 + ε, which isNOT optimal.

Objective

Feasible Region

Optimal Vertex

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Page 70: Is Multipath Routing Really a Panacea?

Science and Engineering in Network Management

Are we always swayed by our drive to get a “better”approach?– Engineering

Are we forgetting to study a system as it is?– Science

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Page 71: Is Multipath Routing Really a Panacea?

Science and Engineering in Network Management

Are we always swayed by our drive to get a “better”approach?– Engineering

Are we forgetting to study a system as it is?– Science

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Page 72: Is Multipath Routing Really a Panacea?

Summary

Back to the original question: Is it a Panacea?It depends:)For networks N ≤ 25 with all pair traffic, it’s reasonablybeneficialThe benefit of multipath routing diminishes as N increasesand L = O(N) [realistic ISP topologies]If N ≈ 100, the benefit is quite minimal.MPM∗ observed is much lower than theoretical MPMThe objective function is not an impacting factorD + L result is traffic/capacity invariant.Science of a Network Management problem is important toinvestigate!

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Page 73: Is Multipath Routing Really a Panacea?

Thank You!

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Page 74: Is Multipath Routing Really a Panacea?

What about TCP Throughput?

TCP throughput problem is modeled as a utilitymaximization problem:

maxx≥0,X≥0

∑d∈D

wd log Xd

subject to∑

p∈Pd

xdp = Xd , d ∈ D∑d∈D

∑p∈Pd

δdp` xdp ≤ c`, ` ∈ L(7)

There are D + L constraintsWe can see that the objective is non-linear concave; wecan use the piece-linear approximation trick.That is, the D + L property holds

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Page 75: Is Multipath Routing Really a Panacea?

X. Liu, S. Mohanraj, M. Pioro, and D. Medhi, “MultipathRouting from a Traffic Engineering Perspective: HowBeneficial is It?”, Proc. of 22nd IEEE InternationalConference on Network Protocols (ICNP), The ResearchTriangle, North Carolina, October 2014.http://sce2.umkc.edu/csee/dmedhi/papers/lmpm-icnp-2014.pdf

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